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Register a new userTests of Sunspot Number Sequences: 2. Using Geomagnetic and Auroral Data
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Mike Lockwood Prof.
Publication date
2016
fields
Physics
and research's language is
English
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We compare four sunspot-number data sequences against geomagnetic and terrestrial auroral observations. The comparisons are made for the original SIDC composite of Wolf-Zurich-International sunspot number [$R_{ISNv1}$], the group sunspot number [$R_{G}$] by Hoyt and Schatten (Solar Phys., 1998), the new backbone group sunspot number [$R_{BB}$] by Svalgaard and Schatten (Solar Phys., 2016), and the corrected sunspot number [$R_{C}$] by Lockwood at al. (J.G.R., 2014). Each sunspot number is fitted with terrestrial observations, or parameters derived from terrestrial observations to be linearly proportional to sunspot number, over a 30-year calibration interval of 1982-2012. The fits are then used to compute test sequences, which extend further back in time and which are compared to $R_{ISNv1}$, $R_{G}$, $R_{BB}$, and $R_{C}$. To study the long-term trends, comparisons are made using averages over whole solar cycles (minimum-to-minimum). The test variations are generated in four ways: i) using the IDV(1d) and IDV geomagnetic indices (for 1845-2013) fitted over the calibration interval using the various sunspot numbers and the phase of the solar cycle; ii) from the open solar flux (OSF) generated for 1845 - 2013 from four pairings of geomagnetic indices by Lockwood et al. (Ann. Geophys., 2014) and analysed using the OSF continuity model of Solanki at al. (Nature, 2000) which employs a constant fractional OSF loss rate; iii) the same OSF data analysed using the OSF continuity model of Owens and Lockwood (J.G.R., 2012) in which the fractional loss rate varies with the tilt of the heliospheric current sheet and hence with the phase of the solar cycle; iv) the occurrence frequency of low-latitude aurora for 1780-1980 from the survey of Legrand and Simon (Ann. Geophys., 1987). For all cases, $R_{BB}$ exceeds the test terrestrial series by an amount that increases as one goes back in time.
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More than 70 years ago it was recognised that ionospheric F2-layer critical frequencies $foF2$ had a strong relationship to sunspot number. Using historic datasets from the Slough and Washington ionosondes, we evaluate the best statistical fits of $foF2$ to sunspot numbers (at each Universal Time [UT] separately) in order to search for drifts and abrupt changes in the fit residuals over Solar Cycles 17 - 21. Polynomial fits are made both with and without allowance for the white-light facular area, which has been reported as being associated with cycle-to-cycle changes in the sunspot number - $foF2$ relationship. Over the interval studied here, the ISN, $R$, the backbone group number $Rbb$, and the corrected number $Rc$ largely differ in their allowance for the Waldmeier discontinuity around 1945 (the correction factor for which for $R$, $Rbb$ and $Rc$ is, respectively, zero, effectively over 20%, and explicitly 11.6%). It is shown that for Solar Cycles 18 - 21, all three sunspot data sequences perform well, but that the fit residuals are lowest and most uniform for $Rbb$. We here use $foF2$ for those UTs for which $R$, $Rbb$, and $Rc$ all give correlations exceeding 0.99 for intervals both before and after the Waldmeier discontinuity. The error introduced by the Waldmeier discontinuity causes $R$ to underestimate the fitted values based on the $foF2$ data for 1932 - 1945 but $Rbb$ overestimates them by almost the same factor, implying that the correction for the Waldmeier discontinuity inherent in $Rbb$ is too large by a factor of two. Fit residuals are smallest and most uniform for $Rc$ and the ionospheric data support the optimum discontinuity multiplicative correction factor derived from the independent Royal Greenwich Observatory (RGO) sunspot group data for the same interval.
We use 5 test data series to quantify putative discontinuities around 1946 in 5 annual-mean sunspot number or group number sequences. The series tested are: the original and n
We use sunspot group observations from the Royal Greenwich Observatory (RGO) to investigate the effects of intercalibrating data from observers with different visual acuities. The tests are made by counting the number of groups $R_B$ above a variable cut-off threshold of observed total whole-spot area (uncorrected for foreshortening) to simulate what a lower acuity observer would have seen. The synthesised annual means of $R_B$ are then re-scaled to the observed RGO group number $R_A$ using a variety of regression techniques. It is found that a very high correlation between $R_A$ and $R_B$ ($r_{AB}$ > 0.98) does not prevent large errors in the intercalibration (e.g. sunspot maximum values can be over 30% too large even for such levels of $r_{AB}$). In generating the backbone sunspot number, Svalgaard and Schatten [2015] force regression fits to pass through the scatter plot origin which generates unreliable fits (the residuals do not form a normal distribution) and causes sunspot cycle amplitudes to be exaggerated in the intercalibrated data. It is demonstrated that the use of Quantile-Quantile (Q-Q) plots to test for a normal distribution is a useful indicator of erroneous and misleading regression fits. Ordinary least squares linear fits, not forced to pass through the origin, are sometimes reliable (although the optimum method used is shown to be different when matching peak and average sunspot group numbers). However other fits are only reliable if non-linear regression is used. From these results it is entirely possible that the inflation of solar cycle amplitudes in the backbone group sunspot number as one goes back in time, relative to related solar-terrestrial parameters, is entirely caused by the use of inappropriate and non-robust regression techniques to calibrate the sunspot data.
New sunspot data composites, some of which are radically different in the character of their long-term variation, are evaluated over the interval 1845-2014. The method commonly used to calibrate historic sunspot data, relative to modern-day data, is daisy-chaining, whereby calibration is passed from one data subset to the neighbouring one, usually using regressions of the data subsets for the intervals of their overlap. Recent studies have illustrated serious pitfalls in these regressions and the resulting errors can be compounded by their repeated use as the data sequence is extended back in time. Hence the recent composite data series by Usoskin et al. (2016), $R_{UEA}$, is a very important advance because it avoids regressions, daisy-chaining and other common, but invalid, assumptions: this is achieved by comparing the statistics of active day fractions to those for a single reference dataset. We study six sunspot data series including $R_{UEA}$ and the new backbone data series $R_{BB}$, recently generated by Svalgaard and Schatten (2016) by employing both regression and daisy-chaining. We show that all six can be used with a continuity model to reproduce the main features of the open solar flux variation for 1845-2014, as reconstructed from geomagnetic activity data. However, some differences can be identified that are consistent with tests using a basket of other proxies for solar magnetic fields. Using data from a variety of sunspot observers, we illustrate problems with the method employed in $R_{BB}$ which cause it to increasingly overestimate sunspot numbers going back in time and we recommend using $R_{UEA}$ because it employs more robust procedures that avoid such problems.
The Sun exhibits a well-observed modulation in the number of spots on its disk over a period of about 11 years. From the dawn of modern observational astronomy sunspots have presented a challenge to understanding -- their quasi-periodic variation in number, first noted 175 years ago, stimulates community-wide interest to this day. A large number of techniques are able to explain the temporal landmarks, (geometric) shape, and amplitude of sunspot cycles, however forecasting these features accurately in advance remains elusive. Recent observationally-motivated studies have illustrated a relationship between the Suns 22-year (Hale) magnetic cycle and the production of the sunspot cycle landmarks and patterns, but not the amplitude of the sunspot cycle. Using (discrete) Hilbert transforms on more than 270 years of (monthly) sunspot numbers we robustly identify the so-called termination events that mark the end of the previous 11-yr sunspot cycle, the enhancement/acceleration of the present cycle, and the end of 22-yr magnetic activity cycles. Using these we extract a relationship between the temporal spacing of terminators and the magnitude of sunspot cycles. Given this relationship and our prediction of a terminator event in 2020, we deduce that Sunspot Cycle 25 could have a magnitude that rivals the top few since records began. This outcome would be in stark contrast to the community consensus estimate of sunspot cycle 25 magnitude.
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